Structural identifiability of PK/PD models
Structural identifiability asks whether the parameters of a model can be determined uniquely from ideal, noise-free data of the chosen outputs. It depends on the model and the design, not on the data collected.
Definition
A parameter is structurally identifiable if, with continuous, noise-free observation of the chosen model outputs after known doses, only one value of it reproduces the output. If many values give exactly the same output, the parameter is not identifiable, however much data are collected.
This depends only on the model structure, the observed outputs and the doses. It says nothing about noise or sampling times.
Example: V/F
After oral dosing with no intravenous data, the bioavailability F cannot be separated from the volume V and the clearance CL. Only combinations such as V/F and CL/F can be determined. Fitting V and F separately then gives arbitrary values, and the fit reports a model that looks well determined when it is not.
Why it matters
Checking structural identifiability before fitting tells whether a flat likelihood or an unstable estimate comes from the model itself. If it does, collecting more of the same data does not help; the model or the measured outputs have to change.
Software
The R package pkident checks structural identifiability of PK/PD ODE models built on rxode2, and compares two independent structural methods. Practical identifiability, the case with real noisy data, is a separate question: see practical identifiability.
Frequently asked questions
Does structural identifiability guarantee good parameter estimates?
No. It is a property of the model under ideal data. With noisy, sparse data, parameters that are structurally identifiable can still be poorly estimated; that is practical identifiability.
Why can only V/F be determined after oral dosing?
Without intravenous data, the bioavailability F scales the dose that reaches the circulation in the same way as a change in volume, so F and V cannot be separated; only V/F and CL/F can be determined.